ECE-GY 6113 Ivan Selesnick
DSP 1
Inverse Systems, ECG data (Matlab exercises)
1) An ECG signal x is processed by an LTI system H implemented as the difference
equation:
y(n) = x(n) + 0.5 x(n-1) + 0.8 y(n-1).
The output signal y is available in the accompanying file ecg_distorted_1.txt. This
difference equation was implemented by the following Matlab code fragment.
b = [1 0.5];
a = [1 -0.8];
y = filter(b, a, x);
save('ecg_distorted_1.txt', 'y', '-ascii');
Your task is to recover the signal x. Derive and implement a stable inverse system G.
Using your inverse system, numerically find the ECG signal x. Submit your derivation of
the inverse system, and plot the ECG signal x. Show the impulse response h and the
convolutional inverse g. Verify the convolution of h and g is an impulse.
2) Same as previous Exercise (1) except the LTI system H is different and the data file
is different. An ECG signal x is processed by the difference equation:
y(n) = 0.5 x(n) + x(n-1) + 0.8 y(n-1).
The output signal y is available in the accompanying file ecg_distorted_2.txt. This was
implemented in Matlab as:
b = [0.5 1];
a = [1 -0.8];
y = filter(b, a, x);
save('ecg_distorted_2.txt', 'y', '-ascii');
Your task is to recover the signal x. Derive and implement a stable inverse system G.
Using your inverse system, numerically find the ECG signal x. Submit your derivation of
the inverse system, and plot the ECG signal x. Show the impulse response h and the
convolutional inverse g. Verify the convolution of h and g is an impulse.